This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. Primary support for the subproject and the subproject's principal investigator may have been provided by other sources, including other NIH sources. The Total Cost listed for the subproject likely represents the estimated amount of Center infrastructure utilized by the subproject, not direct funding provided by the NCRR grant to the subproject or subproject staff. The objective of this research is the automatic code generation and optimization of discrete Fourier transform (DFT) libraries for supercomputer platforms. Most current high performance parallel implementations of the DFT (and its variants) for various platforms are typically hand-coded and manually tuned to work for a single transform/size, and are constrained to specific data formats. Our goal is to automate the process of generating high-performance DFT libraries for a wide variety of problem specifications and scenarios for supercomputing platforms. Our approach uses algorithmic manipulation at a high level of abstraction, based on a set of mathematical rules, which allows automation of library generation. The Fourier transform is a compute kernel that is used extensively in scientific computing, including biomedical image processing.